Lecture 01: Introduction and Foundations
PUBH 8878, Statistical Genetics
About Me
- I’m Chiraag Gohel, a 4th Year PhD student in the Department of Biostatistics and Bioinformatics at George Washington University.
- My interests are in the modeling of high-dimensional ’omics data
- I play a lot of squash
What is statistical genetics?
What does the data look like?
Family/Pedigree Studies
Family/Pedigree Studies
What does the data look like?
Genome-Wide Association Studies (GWAS)
Genome-Wide Association Studies
Core abstractions for quantitative biology
- Model-Building
- Formulate generative models linking genotype, environment, and phenotype (e.g., linear mixed, Bayesian hierarchical, non-parametric kernels).
- Encode biological structure: linkage & LD, population stratification, dominance/epistasis, multi-omics priors.
- Balance realism and tractability to enable scalable computation on genome-scale data.
Core abstractions for quantitative biology
- Inference
- Estimate unknown parameters and latent effects via likelihood maximisation, EM, MCMC, or SGD
- Quantify uncertainty with standard errors, posterior intervals, and credible sets
- Control false discoveries across millions of tests with FDR/Q-value, permutation, and empirical-Bayes shrinkage.
Core abstractions for quantitative biology
- Prediction
- Use fitted models for out-of-sample trait prediction: BLUP/GBLUP, ridge/lasso/elastic-net, Bayesian whole-genome regressions, random forests, neural nets.
- Evaluate accuracy (MSE, AUC), bias–variance trade-off, calibration, and portability across ancestries or cell types.
- Translate genomic predictions into actionable scores for breeding, risk stratification, and drug-target prioritisation.
Core abstractions for quantitative biology
- Interpretation & Validation
- Integrate functional annotations, eQTL, and single-cell data to refine biological mechanisms.
- Perform replication, cross-cohort meta-analysis, and sensitivity analyses to population assumptions.
- Communicate findings with clear visualisations and reproducible workflows (R/Bioconductor, Git, notebooks).
Early work in the field
Genetics, statistics, and eugenics, have always been closely linked
The ethics of genetics and genomics is/(was) of great importance!
Parameter Estimation
- Imagine a geneticist is studying allele ages (i.e., how many generations ago an allele arose via mutation) under a simplified model where new mutations arise randomly and uniformly over a fixed window — say, the last \(\theta\) generations.
- We could model \(\theta \sim \textsf{Uniform}(0, \theta)\).
- We have our observed sample \(\{x_1,x_2, \ldots, x_n\}\), ages in generations of \(n\) observed alleles.
- For concreteness, let our sample be \(\{0, 1, 8, 4, 3, 1, 1, 5\}\).
- How should we estimate \(\theta\) ?
Importance of statistical theory
- Understanding random variables, sampling distributions, and bias/variance of estimators helps motivate biological questions, and understand how they can be answered
- Let y be the expression of a trait, G be the additive contribution of genetic variables, and an environmental value E;
- What assumptions do we make via the following models?
\[\begin{align} y &= G + E \\ y &= \beta_0 + \beta_1 G + \beta_2 E + \epsilon \\ y &= \beta_0 + \beta_1 G + \beta_2 E + \epsilon, \quad \epsilon \sim N(0, \sigma^2) \\ y &= \beta_0 + \beta_1 G + \beta_2 E + \beta_3 \left(G \times E\right) + \epsilon, \quad \epsilon \sim N(0, \sigma^2) \end{align}\]
Molecular Genetics
